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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.comp_compilers"></a><a class="link" href="comp_compilers.html" title="Comparing Different Compilers">Comparing Different Compilers</a>
</h2></div></div></div>
<p>
      By running our performance test suite multiple times, we can compare the effect
      of different compilers: as might be expected, the differences are generally
      small compared to say disabling internal use of <code class="computeroutput"><span class="keyword">long</span>
      <span class="keyword">double</span></code>. However, there are still gains
      to be main, particularly from some of the commercial offerings:
    </p>
<div class="table">
<a name="math_toolkit.comp_compilers.table_Compiler_Comparison_on_Windows_x64"></a><p class="title"><b>Table 23.12. Compiler Comparison on Windows x64</b></p>
<div class="table-contents"><table class="table" summary="Compiler Comparison on Windows x64">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              <p>
                Function
              </p>
            </th>
<th>
              <p>
                Microsoft Visual C++ version 14.2<br> boost 1.73
              </p>
            </th>
<th>
              <p>
                GNU C++ version 9.2.0<br> boost 1.73
              </p>
            </th>
<th>
              <p>
                GNU C++ version 9.2.0<br> boost 1.73<br> promote_double&lt;false&gt;
              </p>
            </th>
</tr></thead>
<tbody>
<tr>
<td>
              <p>
                assoc_laguerre
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.41<br> (179ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (137ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (127ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                assoc_legendre
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.76<br> (248ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.36<br> (192ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (141ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                beta
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (123ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.62<br> (322ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.93<br> (237ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                beta (incomplete)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (470ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.95<br> (1385ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.58<br> (741ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cbrt
              </p>
            </td>
<td>
              <p>
                <span class="red">3.40<br> (51ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.67<br> (70ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (15ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_i
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (281ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.38<br> (949ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.38<br> (387ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_i (integer order)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (195ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.06<br> (597ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (195ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_j
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (371ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.39<br> (886ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.35<br> (499ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_j (integer order)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.28<br> (123ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.92<br> (184ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (96ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_k
              </p>
            </td>
<td>
              <p>
                <span class="green">1.11<br> (385ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">19.68<br> (6847ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (348ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_k (integer order)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (217ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">18.17<br> (3724ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (205ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_neumann
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (6696ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.76<br> (10032ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (5715ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_neumann (integer order)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (158ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.20<br> (348ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.59<br> (252ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                digamma
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (20ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.45<br> (69ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.30<br> (46ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_1
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.57<br> (390ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.41<br> (349ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (248ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_1 (complete)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.64<br> (77ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.64<br> (77ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (47ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_2
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.81<br> (702ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.50<br> (583ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (388ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_2 (complete)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.11<br> (84ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.11<br> (57ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (27ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_3
              </p>
            </td>
<td>
              <p>
                <span class="red">3.47<br> (1381ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.68<br> (670ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (398ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_3 (complete)
              </p>
            </td>
<td>
              <p>
                <span class="red">inf<br> (802ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan(ind)<br> (0ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan(ind)<br> (0ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rc
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.55<br> (59ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.21<br> (84ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (38ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rd
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.32<br> (271ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.26<br> (260ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (206ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rf
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (62ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.94<br> (95ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (49ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rj
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.46<br> (264ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.29<br> (414ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (181ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                erf
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.30<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.85<br> (61ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (33ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                erfc
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (54ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.76<br> (90ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (51ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                expint
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (27ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.41<br> (92ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.22<br> (60ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                expint (En)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (106ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.94<br> (206ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.29<br> (137ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                expm1
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (11ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.00<br> (33ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.36<br> (26ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_p
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (303ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">2.00<br> (605ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (355ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_p_inv
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1266ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.85<br> (2341ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.15<br> (1460ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_q
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (294ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.10<br> (618ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (356ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_q_inv
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1194ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.66<br> (1987ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.14<br> (1357ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibeta
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (512ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.63<br> (1344ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (673ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibeta_inv
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1910ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.49<br> (4751ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.48<br> (2822ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibetac
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (525ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.60<br> (1365ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (668ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibetac_inv
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1676ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.85<br> (4778ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.74<br> (2910ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                jacobi_cn
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (181ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.10<br> (561ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">2.00<br> (362ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                jacobi_dn
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (203ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.03<br> (616ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.93<br> (392ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                jacobi_sn
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (202ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.81<br> (568ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.73<br> (350ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                laguerre
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (107ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.07<br> (112ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (105ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                legendre
              </p>
            </td>
<td>
              <p>
                <span class="green">1.11<br> (283ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.25<br> (320ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (255ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                legendre Q
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (309ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.51<br> (466ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.15<br> (354ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                lgamma
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (80ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.67<br> (214ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">2.00<br> (160ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                log1p
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (14ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.07<br> (29ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (17ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                polygamma
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (4193ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.85<br> (7743ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.91<br> (8018ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                sph_bessel
              </p>
            </td>
<td>
              <p>
                <span class="green">1.01<br> (668ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.48<br> (975ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (661ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                sph_neumann
              </p>
            </td>
<td>
              <p>
                <span class="green">1.07<br> (1138ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.96<br> (3153ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1064ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                tgamma
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (74ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.50<br> (259ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.14<br> (158ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                tgamma (incomplete)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (208ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.30<br> (478ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.64<br> (342ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                trigamma
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (12ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.83<br> (34ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (14ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                zeta
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (117ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.65<br> (310ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.89<br> (221ns)</span>
              </p>
            </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="math_toolkit.comp_compilers.table_Compiler_Comparison_on_linux"></a><p class="title"><b>Table 23.13. Compiler Comparison on linux</b></p>
<div class="table-contents"><table class="table" summary="Compiler Comparison on linux">
<colgroup>
<col>
<col>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              <p>
                Function
              </p>
            </th>
<th>
              <p>
                GNU C++ version 9.2.1 20191008<br> boost 1.73
              </p>
            </th>
<th>
              <p>
                GNU C++ version 9.2.1 20191008<br> boost 1.73<br> promote_double&lt;false&gt;
              </p>
            </th>
<th>
              <p>
                Clang version 9.0.0 (tags/RELEASE_900/final)<br> boost 1.73
              </p>
            </th>
<th>
              <p>
                Clang version 9.0.0 (tags/RELEASE_900/final)<br> boost 1.73<br>
                promote_double&lt;false&gt;
              </p>
            </th>
<th>
              <p>
                Intel C++ C++0x mode version 1910<br> boost 1.73
              </p>
            </th>
<th>
              <p>
                Intel C++ C++0x mode version 1910<br> boost 1.73<br> promote_double&lt;false&gt;
              </p>
            </th>
</tr></thead>
<tbody>
<tr>
<td>
              <p>
                assoc_laguerre
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (156ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (143ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.72<br> (229ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (174ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.15<br> (153ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (133ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                assoc_legendre
              </p>
            </td>
<td>
              <p>
                <span class="red">2.91<br> (279ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.78<br> (171ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.86<br> (275ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (96ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.79<br> (268ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.16<br> (207ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                beta
              </p>
            </td>
<td>
              <p>
                <span class="red">10.52<br> (789ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.40<br> (105ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">10.56<br> (792ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.73<br> (130ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">6.07<br> (455ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (75ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                beta (incomplete)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.98<br> (2076ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.26<br> (524ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.44<br> (2267ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (417ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.15<br> (1315ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.16<br> (484ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cbrt
              </p>
            </td>
<td>
              <p>
                <span class="red">2.52<br> (58ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.09<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.35<br> (54ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.22<br> (28ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.91<br> (44ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_i
              </p>
            </td>
<td>
              <p>
                <span class="red">5.05<br> (1182ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (239ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">10.73<br> (2511ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.74<br> (406ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.99<br> (933ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (234ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_i (integer order)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.41<br> (767ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (174ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.09<br> (886ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (179ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.63<br> (631ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.12<br> (195ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_j
              </p>
            </td>
<td>
              <p>
                <span class="red">3.80<br> (1067ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.28<br> (359ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.72<br> (1327ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.55<br> (436ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.05<br> (857ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (281ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_j (integer order)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.10<br> (319ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.05<br> (108ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.73<br> (487ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (103ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.30<br> (237ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.12<br> (115ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_k
              </p>
            </td>
<td>
              <p>
                <span class="red">10.37<br> (3962ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (382ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">11.55<br> (4414ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.52<br> (582ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">12.41<br> (4739ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.09<br> (416ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_bessel_k (integer order)
              </p>
            </td>
<td>
              <p>
                <span class="red">19.23<br> (3289ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (181ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">19.78<br> (3382ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (217ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">20.02<br> (3423ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (171ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_neumann
              </p>
            </td>
<td>
              <p>
                <span class="red">2.18<br> (8826ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.19<br> (4814ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.23<br> (13059ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (5275ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.35<br> (9503ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (4041ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                cyl_neumann (integer order)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.67<br> (466ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.35<br> (172ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.49<br> (570ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.15<br> (146ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.87<br> (364ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (127ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                digamma
              </p>
            </td>
<td>
              <p>
                <span class="red">2.30<br> (62ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.30<br> (35ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.11<br> (84ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.33<br> (36ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.85<br> (50ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (27ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_1
              </p>
            </td>
<td>
              <p>
                <span class="red">2.26<br> (310ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.12<br> (154ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">6.96<br> (954ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.25<br> (171ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.22<br> (441ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (137ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_1 (complete)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.65<br> (93ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.15<br> (63ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">6.00<br> (120ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.15<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.90<br> (38ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (20ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_2
              </p>
            </td>
<td>
              <p>
                <span class="red">3.81<br> (704ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.28<br> (236ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">8.95<br> (1655ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.36<br> (251ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.36<br> (807ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (185ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_2 (complete)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.83<br> (44ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">6.25<br> (150ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.25<br> (30ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">2.00<br> (48ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (24ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_3
              </p>
            </td>
<td>
              <p>
                <span class="red">3.27<br> (609ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (217ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.37<br> (998ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.32<br> (245ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.84<br> (528ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (186ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_3 (complete)
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan<br> (0ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan<br> (0ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan<br> (0ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan<br> (0ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan<br> (0ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">-nan<br> (0ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rc
              </p>
            </td>
<td>
              <p>
                <span class="red">2.75<br> (66ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.29<br> (31ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.71<br> (113ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.42<br> (34ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.83<br> (44ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (24ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rd
              </p>
            </td>
<td>
              <p>
                <span class="red">4.37<br> (428ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (128ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">9.24<br> (906ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (128ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.17<br> (409ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (98ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rf
              </p>
            </td>
<td>
              <p>
                <span class="red">2.47<br> (84ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.44<br> (49ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.62<br> (157ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.32<br> (45ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.85<br> (63ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (34ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ellint_rj
              </p>
            </td>
<td>
              <p>
                <span class="red">4.14<br> (426ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.36<br> (140ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">7.18<br> (740ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (135ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.33<br> (343ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (103ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                erf
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.69<br> (54ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.28<br> (41ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.56<br> (82ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.38<br> (44ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.34<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (32ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                erfc
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.65<br> (89ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.20<br> (65ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.46<br> (133ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.26<br> (68ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.22<br> (66ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (54ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                expint
              </p>
            </td>
<td>
              <p>
                <span class="red">2.93<br> (85ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.45<br> (42ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.90<br> (84ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (38ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.21<br> (64ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (29ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                expint (En)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.42<br> (242ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.14<br> (114ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.76<br> (276ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.19<br> (119ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.84<br> (184ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (100ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                expm1
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.90<br> (19ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.60<br> (16ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.50<br> (15ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.40<br> (14ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.80<br> (18ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (10ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_p
              </p>
            </td>
<td>
              <p>
                <span class="red">2.43<br> (618ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (260ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.95<br> (749ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (254ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.15<br> (545ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (262ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_p_inv
              </p>
            </td>
<td>
              <p>
                <span class="red">2.37<br> (2328ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (1038ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.73<br> (2676ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (1045ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.92<br> (1883ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (982ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_q
              </p>
            </td>
<td>
              <p>
                <span class="red">2.49<br> (629ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (253ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.28<br> (831ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.11<br> (280ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.18<br> (551ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (263ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                gamma_q_inv
              </p>
            </td>
<td>
              <p>
                <span class="red">2.73<br> (2016ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.30<br> (958ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.22<br> (2381ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.30<br> (962ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.73<br> (1275ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (739ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibeta
              </p>
            </td>
<td>
              <p>
                <span class="red">4.56<br> (1979ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (524ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.60<br> (1996ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (434ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.35<br> (1453ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.13<br> (491ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibeta_inv
              </p>
            </td>
<td>
              <p>
                <span class="red">3.22<br> (5552ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.10<br> (1902ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.49<br> (6013ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (1781ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.58<br> (4437ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1722ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibetac
              </p>
            </td>
<td>
              <p>
                <span class="red">4.34<br> (2008ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (590ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.34<br> (2008ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (463ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.11<br> (1438ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (543ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ibetac_inv
              </p>
            </td>
<td>
              <p>
                <span class="red">3.32<br> (5533ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.11<br> (1853ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.55<br> (5915ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (1722ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.48<br> (4131ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1666ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                jacobi_cn
              </p>
            </td>
<td>
              <p>
                <span class="red">3.74<br> (483ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.26<br> (163ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.98<br> (643ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.61<br> (208ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.67<br> (345ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (129ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                jacobi_dn
              </p>
            </td>
<td>
              <p>
                <span class="red">3.64<br> (503ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.25<br> (173ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.70<br> (648ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.49<br> (206ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.72<br> (375ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (138ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                jacobi_sn
              </p>
            </td>
<td>
              <p>
                <span class="red">4.99<br> (614ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.46<br> (180ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.20<br> (640ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.72<br> (212ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.57<br> (316ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (123ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                laguerre
              </p>
            </td>
<td>
              <p>
                <span class="green">1.11<br> (92ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (90ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.41<br> (117ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.11<br> (92ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (97ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (83ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                legendre
              </p>
            </td>
<td>
              <p>
                <span class="green">1.12<br> (282ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (251ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (304ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.30<br> (326ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.39<br> (349ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (270ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                legendre Q
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (390ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (314ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.29<br> (404ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.14<br> (358ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.42<br> (445ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.11<br> (347ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                lgamma
              </p>
            </td>
<td>
              <p>
                <span class="red">2.65<br> (265ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (117ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.86<br> (386ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (124ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.90<br> (190ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (100ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                log1p
              </p>
            </td>
<td>
              <p>
                <span class="green">1.11<br> (20ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.22<br> (22ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (19ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (18ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.06<br> (19ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (18ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                polygamma
              </p>
            </td>
<td>
              <p>
                <span class="red">16.70<br> (8883ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.42<br> (756ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">6.56<br> (3491ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (532ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">7.49<br> (3985ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.05<br> (559ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                sph_bessel
              </p>
            </td>
<td>
              <p>
                <span class="red">2.36<br> (1122ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (588ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.31<br> (1574ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.41<br> (673ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.12<br> (1010ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (476ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                sph_neumann
              </p>
            </td>
<td>
              <p>
                <span class="red">3.40<br> (2842ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (1015ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.59<br> (3009ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (1012ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.14<br> (2627ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (837ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                tgamma
              </p>
            </td>
<td>
              <p>
                <span class="red">4.72<br> (472ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.44<br> (144ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.70<br> (570ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.05<br> (105ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.29<br> (229ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (100ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                tgamma (incomplete)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.28<br> (669ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.13<br> (231ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">3.88<br> (792ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.14<br> (232ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.21<br> (451ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (204ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                trigamma
              </p>
            </td>
<td>
              <p>
                <span class="red">2.08<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (12ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">4.00<br> (48ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.50<br> (18ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">2.00<br> (24ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (13ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                zeta
              </p>
            </td>
<td>
              <p>
                <span class="red">4.21<br> (455ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (108ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">5.77<br> (623ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.20<br> (130ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.98<br> (322ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (117ns)</span>
              </p>
            </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
      Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
      Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
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